How to model vertical cross horizontal lines to become look like torus ? 3D printing
create a pretty high density torus, (i used 128 and 32 major and minor segments, respectively). You might need to add and apply a 1 level subdivision surface modifier if the density was not high enough (in my case, this was necessary).



Tab into edit mode and select any edge loop, go to the select pop up list and choose "Checker deselect".

Hit Ctrl+E and click "Edge Rings", then Ctrl-click the face select icon, on the bottom left of your screen.



Hit the X key and use the "Faces" option.

Now you'll want to go to the select panel once again and pick the "Random" selection tool, then hit F6 and find a nice percentage (i used 2%) and finally hit X and choose the "Faces" option.



You'll now be making use of the "Random" selection tool for the last time, make sure to use a percentage that works for you (i used 0.5%). Hit Ctrl+L and then X and choose the "faces" option.



If you followed the steps properly so far you should have face loops that follow the shape of a torus with irregularly placed gaps.

Now tab out to Object mode and repeat the process but for the faces perpendicular to the ones you just got.

Select both objects and hit Ctrl+J to join them. Tab into edit mode, select everything using the A key then hit Ctrl+V and choose the "Remove Doubles" option.



Tab back out to Object mode and add a Solidify modifier, followed by a subdivision surface modifier.